Metrics for Herbie run

Date:	Saturday, May 25th, 2024
Commit:	445b0ec4 on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024146
Parameters:	256 points for 4 iterations
Flags:	`localize:costslocalize:errorsreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default

sample5.7min (32.5%)

Results

2.0min	25933×	5	exit
1.2min	129782×	1	valid
43.4s	270634×	0	valid
23.0s	8237×	3	valid
18.9s	19236×	2	valid
14.3s	49639×	0	unsamplable
8.2s	1422×	4	valid
4.1s	19059×	0	invalid
3.3s	11057×	1	invalid
1.3s	1692×	2	invalid
99.0ms	863×	0	precondition
51.0ms	53×	1	unsamplable
14.0ms	23×	3	invalid
4.0ms	1×	2	unsamplable
2.0ms	1×	5	valid

Precisions

Click to see histograms. Total time spent on operations: 4.5min

ival-pow: 1.9min (42.3% of total)

ival-mult: 25.8s (9.6% of total)

ival-sin: 22.9s (8.5% of total)

ival-cos: 22.3s (8.3% of total)

backward-pass: 17.9s (6.6% of total)

ival-div: 16.5s (6.1% of total)

ival-add: 9.8s (3.6% of total)

ival-sub: 8.9s (3.3% of total)

ival-log: 6.1s (2.3% of total)

ival-exp: 5.6s (2.1% of total)

ival-sqrt: 4.9s (1.8% of total)

ival-neg: 4.0s (1.5% of total)

ival-<: 2.8s (1% of total)

...c/correct-round.rkt:121:19: 2.2s (0.8% of total)

ival-pi: 1.2s (0.4% of total)

const: 1.0s (0.4% of total)

ival-atan2: 929.0ms (0.3% of total)

ival-tan: 553.0ms (0.2% of total)

ival-acos: 449.0ms (0.2% of total)

ival-atan: 447.0ms (0.2% of total)

ival-and: 425.0ms (0.2% of total)

ival-cbrt: 421.0ms (0.2% of total)

ival-<=: 241.0ms (0.1% of total)

ival-asin: 197.0ms (0.1% of total)

ival-fabs: 158.0ms (0.1% of total)

ival-==: 2.0ms (0% of total)

ival-or: 0.0ms (0% of total)

Bogosity

simplify2.8min (15.7%)

Algorithm

443×	egg-herbie

Rules

171114×	`fma-define`
120423×	`fma-neg`
97357×	`distribute-lft-in`
93134×	`times-frac`
89507×	`*-commutative`

Stop Event

116×	saturated
326×	node limit
1×	unsound

Counts

145197 → 121568

soundness1.8min (10.3%)

Rules

83354×	`fma-define`
63790×	`log1p-expm1-u`
52903×	`times-frac`
51114×	`expm1-log1p-u`
48880×	`distribute-lft-in`

Stop Event

15×	saturated
43×	fuel
253×	node limit
3×	unsound
8×	done

Compiler

Compiled 70894 to 20104 computations (71.6% saved)

localize1.6min (9%)

Results

24.7s	13785×	1	valid
19.2s	2021×	5	exit
12.4s	26348×	0	valid
8.7s	2267×	2	valid
3.6s	555×	3	valid
2.9s	4535×	0	invalid
1.4s	455×	1	invalid
939.0ms	98×	4	valid
473.0ms	90×	2	invalid
193.0ms	10×	5	valid
73.0ms	12×	3	invalid

Compiler

Compiled 95809 to 7579 computations (92.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.4s

ival-mult: 9.3s (18.5% of total)

ival-pow: 7.2s (14.2% of total)

ival-sin: 6.8s (13.6% of total)

backward-pass: 5.5s (10.8% of total)

ival-cos: 4.9s (9.8% of total)

ival-div: 4.0s (7.9% of total)

ival-sub: 1.7s (3.3% of total)

ival-add: 1.6s (3.2% of total)

ival-exp: 1.4s (2.8% of total)

ival-log: 1.1s (2.2% of total)

ival-sqrt: 1.1s (2.2% of total)

ival-hypot: 1.1s (2.1% of total)

...c/correct-round.rkt:121:19: 939.0ms (1.9% of total)

ival-fma: 916.0ms (1.8% of total)

ival-log1p: 618.0ms (1.2% of total)

ival-neg: 468.0ms (0.9% of total)

ival-atan2: 368.0ms (0.7% of total)

ival-cbrt: 317.0ms (0.6% of total)

ival-expm1: 234.0ms (0.5% of total)

const: 220.0ms (0.4% of total)

ival-acos: 173.0ms (0.3% of total)

ival-atan: 167.0ms (0.3% of total)

ival-pi: 118.0ms (0.2% of total)

ival-tan: 95.0ms (0.2% of total)

ival-fabs: 90.0ms (0.2% of total)

ival-asin: 19.0ms (0% of total)

ival-e: 2.0ms (0% of total)

ival-sinh: 1.0ms (0% of total)

regimes1.0min (5.9%)

Counts

29136 → 1011

Calls

155 calls:

4.2s	phi1
3.9s	phi2
3.8s	lambda1
3.8s	lambda2
2.9s	(-.f64 lambda1 lambda2)

Compiler

Compiled 13707 to 8929 computations (34.9% saved)

rewrite55.1s (5.2%)

Algorithm

195×	batch-egg-rewrite

Rules

118636×	`log1p-expm1-u`
93997×	`expm1-log1p-u`
53198×	`pow1`
49650×	`add-exp-log`
46849×	`add-log-exp`

Stop Event

192×	node limit
3×	unsound

Counts

2989 → 76620

prune53.7s (5.1%)

Counts: 194937 → 8740
Compiler: Compiled 632556 to 301505 computations (52.3% saved)

eval41.7s (3.9%)

Compiler: Compiled 9378980 to 876043 computations (90.7% saved)

series39.1s (3.7%)

Counts

2989 → 68577

Calls

17268 calls:

Time	Variable		Point	Expression
924.0ms	angle	@	inf	(log (pow (exp (/ y-scale (* (* 2 (- (pow b 2) (pow a 2))) (/ (cos (* angle (* (PI) 1/180))) x-scale)))) (/ (- (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)) (+ (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (sqrt (+ (* (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2))) (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)))) (* (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))) (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale)))))))) (sin (* angle (* (PI) 1/180))))))
451.0ms	angle	@	0	(log (pow (exp (/ y-scale (* (* 2 (- (pow b 2) (pow a 2))) (/ (cos (* angle (* (PI) 1/180))) x-scale)))) (/ (- (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)) (+ (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (sqrt (+ (* (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2))) (- (* (pow (sqrt (+ (* (* a (sin (* angle (* (PI) 1/180)))) (* a (sin (* angle (* (PI) 1/180))))) (* (* (cos (* angle (* (PI) 1/180))) b) (* (cos (* angle (* (PI) 1/180))) b)))) 2) (pow x-scale -2)) (* (pow (sqrt (+ (* (* a (cos (* angle (* (PI) 1/180)))) (* a (cos (* angle (* (PI) 1/180))))) (* (* b (sin (* angle (* (PI) 1/180)))) (* b (sin (* angle (* (PI) 1/180))))))) 2) (pow y-scale -2)))) (* (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))) (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale)))))))) (sin (* angle (* (PI) 1/180))))))
411.0ms	c_p	@	0	(* c_p (neg (log (+ 1 (exp s)))))
364.0ms	a	@	inf	(log (* a (sin (* angle (* (PI) 1/180)))))
318.0ms	b	@	0	(* (* b (* (pow a 2) (neg b))) (log (exp (* 8 (* (* b (* (pow a 2) (/ (neg b) (pow (* x-scale y-scale) 2)))) (+ (/ (+ (pow (* a (sin (* angle (* 1/180 (PI))))) 2) (pow (* b (cos (* angle (* 1/180 (PI))))) 2)) (pow x-scale 2)) (- (/ (+ (pow (* a (cos (* angle (* 1/180 (PI))))) 2) (pow (* b (sin (* angle (* 1/180 (PI))))) 2)) (pow y-scale 2)) (sqrt (+ (* (- (/ (+ (pow (* a (sin (* angle (* 1/180 (PI))))) 2) (pow (* b (cos (* angle (* 1/180 (PI))))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (* 1/180 (PI))))) 2) (pow (* b (sin (* angle (* 1/180 (PI))))) 2)) (pow y-scale 2))) (- (/ (+ (pow (* a (sin (* angle (* 1/180 (PI))))) 2) (pow (* b (cos (* angle (* 1/180 (PI))))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (* 1/180 (PI))))) 2) (pow (* b (sin (* angle (* 1/180 (PI))))) 2)) (pow y-scale 2)))) (* (* 2 (* (- (pow b 2) (pow a 2)) (* (sin (* angle (* 1/180 (PI)))) (/ (cos (* angle (* 1/180 (PI)))) (* x-scale y-scale))))) (* 2 (* (- (pow b 2) (pow a 2)) (* (sin (* angle (* 1/180 (PI)))) (/ (cos (* angle (* 1/180 (PI)))) (* x-scale y-scale)))))))))))))))

bsearch26.8s (2.5%)

Algorithm

368×	binary-search
91×	left-value

Stop Event

3×	predicate-same
365×	narrow-enough

Results

9.3s	12689×	1	valid
5.8s	31930×	0	valid
2.7s	1176×	3	valid
1.9s	1065×	5	exit
1.5s	1692×	2	valid
330.0ms	49×	4	valid
236.0ms	1131×	0	invalid

Compiler

Compiled 128676 to 87201 computations (32.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.5s

ival-cos: 3.8s (20.8% of total)

ival-sin: 3.4s (18.4% of total)

ival-mult: 2.9s (15.8% of total)

backward-pass: 1.7s (9.3% of total)

ival-pow: 1.6s (8.6% of total)

ival-div: 1.6s (8.4% of total)

ival-sub: 1.1s (5.7% of total)

ival-add: 721.0ms (3.9% of total)

ival-sqrt: 346.0ms (1.9% of total)

ival-atan2: 250.0ms (1.4% of total)

ival-atan: 234.0ms (1.3% of total)

ival-acos: 153.0ms (0.8% of total)

ival-tan: 152.0ms (0.8% of total)

ival-neg: 142.0ms (0.8% of total)

ival-exp: 132.0ms (0.7% of total)

const: 90.0ms (0.5% of total)

ival-pi: 66.0ms (0.4% of total)

ival-log: 60.0ms (0.3% of total)

ival-fabs: 43.0ms (0.2% of total)

ival-asin: 7.0ms (0% of total)

ival-cbrt: 4.0ms (0% of total)

explain26.6s (2.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`#f`	sensitivity	1920	2
`+.f64`	`#f`	cancellation	1704	28
`sin.f64`	`#f`	sensitivity	1664	0
`sqrt.f64`	`#f`	oflow-rescue	1375	0
`-.f64`	`#f`	cancellation	948	11
`-.f64`	`#f`	nan-rescue	639	0
`log.f64`	`#f`	sensitivity	586	0
`/.f64`	`#f`	o/n	471	0
`/.f64`	`#f`	o/o	336	0
`/.f64`	`#f`	u/u	315	0
`*.f64`	`#f`	*no**	224	0
`sqrt.f64`	`#f`	uflow-rescue	171	0
`/.f64`	`#f`	u/n	161	0
`exp.f64`	`#f`	sensitivity	154	23
`/.f64`	`#f`	n/o	122	0
`*.f64`	`#f`	*nu**	104	0
`cbrt.f64`	`#f`	oflow-rescue	86	0
`cbrt.f64`	`#f`	uflow-rescue	46	0
`/.f64`	`#f`	n/u	43	0
`*.f64`	`#f`	*uo**	40	0
`*.f64`	`#f`	*ou**	39	0
`acos.f64`	`(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))`	sensitivity	15	4
`pow.f64`	`#f`	uflow-rescue	7	0
`pow.f64`	`#f`	sensitivity	5	1
`log.f64`	`#f`	oflow-rescue	3	0
`log.f64`	`(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))`	uflow-rescue	2	0
↳	`(+.f64 (exp.f64 a) (exp.f64 b))`	underflow	2
↳	`(exp.f64 a)`	underflow	114
↳	`(exp.f64 b)`	underflow	2

Confusion

	Predicted +	Predicted -
+	5785	62
-	1319	6146

Precision

0.814329954954955

Recall

0.9893962715922695

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5785	31	31
-	1319	28	6118

Precision?

0.811950300153567

Recall?

0.9946981357961348

Freqs

test

number	freq
0	6208
1	4715
2	1552
3	354
4	249
5	144
6	58
7	24
8	5
9	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	43	0	0
-	2	0	7

Precision?

0.9555555555555556

Recall?

1.0

Results

5.3s	8418×	1	valid
3.1s	1882×	2	valid
2.7s	15674×	0	valid
1.8s	566×	3	valid
877.0ms	82×	4	valid
4.0ms	2×	5	valid

Compiler

Compiled 21932 to 3232 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.2s

ival-sin: 2.3s (22.5% of total)

ival-cos: 1.5s (14.8% of total)

ival-mult: 1.3s (12.9% of total)

backward-pass: 1.3s (12.4% of total)

ival-div: 867.0ms (8.5% of total)

ival-pow: 841.0ms (8.3% of total)

ival-sub: 560.0ms (5.5% of total)

ival-add: 415.0ms (4.1% of total)

ival-sqrt: 216.0ms (2.1% of total)

ival-log: 198.0ms (1.9% of total)

ival-exp: 191.0ms (1.9% of total)

ival-neg: 146.0ms (1.4% of total)

ival-pi: 73.0ms (0.7% of total)

const: 61.0ms (0.6% of total)

ival-tan: 54.0ms (0.5% of total)

ival-atan: 46.0ms (0.5% of total)

ival-atan2: 44.0ms (0.4% of total)

ival-asin: 36.0ms (0.4% of total)

ival-cbrt: 30.0ms (0.3% of total)

ival-acos: 22.0ms (0.2% of total)

ival-fabs: 13.0ms (0.1% of total)

analyze23.8s (2.3%)

Algorithm

53×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	79.4%	20.6%	0%	0%	0%	0
14.8%	11.8%	67.6%	20.6%	0%	0%	0%	1
22.6%	17.7%	60.4%	21%	0%	0.9%	0%	2
32.7%	24.7%	50.8%	21.2%	0%	3.3%	0%	3
39.8%	29.8%	45%	21.2%	0%	4%	0%	4
45.4%	33.8%	40.6%	21.2%	0%	4.5%	0%	5
48.4%	35.7%	38%	21.2%	0%	5.1%	0%	6
51.8%	37.8%	35.2%	21.2%	0%	5.7%	0.1%	7
53.5%	38.9%	33.8%	21.3%	0%	6%	0.1%	8
56.4%	40.6%	31.4%	21.3%	0%	6.6%	0.2%	9
57.7%	41.4%	30.3%	21.3%	0%	6.8%	0.2%	10
59.8%	42.7%	28.7%	21.3%	0%	7.1%	0.3%	11
61.3%	43.5%	27.5%	21.3%	0%	7.5%	0.3%	12

Compiler

Compiled 1919 to 947 computations (50.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.4s

ival-mult: 4.7s (30.5% of total)

ival-pow: 2.4s (15.4% of total)

ival-cos: 1.7s (10.9% of total)

ival-sin: 1.3s (8.2% of total)

ival-div: 1.2s (8% of total)

ival-sub: 768.0ms (5% of total)

ival-add: 759.0ms (4.9% of total)

ival-sqrt: 587.0ms (3.8% of total)

...c/correct-round.rkt:121:19: 481.0ms (3.1% of total)

ival-neg: 343.0ms (2.2% of total)

ival-<: 279.0ms (1.8% of total)

ival-atan2: 211.0ms (1.4% of total)

ival-atan: 104.0ms (0.7% of total)

ival-tan: 102.0ms (0.7% of total)

ival-exp: 100.0ms (0.6% of total)

const: 97.0ms (0.6% of total)

ival-pi: 67.0ms (0.4% of total)

ival-log: 58.0ms (0.4% of total)

ival-and: 54.0ms (0.4% of total)

ival-fabs: 48.0ms (0.3% of total)

ival-acos: 36.0ms (0.2% of total)

ival-asin: 35.0ms (0.2% of total)

ival-cbrt: 23.0ms (0.1% of total)

backward-pass: 22.0ms (0.1% of total)

ival-<=: 3.0ms (0% of total)

ival-==: 1.0ms (0% of total)

ival-or: 0.0ms (0% of total)

preprocess15.3s (1.4%)

Algorithm

52×	egg-herbie

Rules

32328×	`fma-define`
19274×	`fma-neg`
13234×	`div-sub`
11584×	`unsub-neg`
11427×	`sub-neg`

Stop Event

22×	saturated
30×	node limit

Compiler

Compiled 70552 to 24876 computations (64.7% saved)

Herbie run

sample5.7min (32.5%)

simplify2.8min (15.7%)

soundness1.8min (10.3%)

localize1.6min (9%)

regimes1.0min (5.9%)

rewrite55.1s (5.2%)

prune53.7s (5.1%)

eval41.7s (3.9%)

series39.1s (3.7%)

bsearch26.8s (2.5%)

explain26.6s (2.5%)

analyze23.8s (2.3%)

preprocess15.3s (1.4%)

end1.0ms (0%)

Profiling