Metrics for Herbie run

Date:	Thursday, May 23rd, 2024
Commit:	6b737c7e on explanations-trifurcate
Hostname:	nightly with Racket 8.11.1
Seed:	2024144
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	25860×	5	exit
1.2min	130062×	1	valid
43.4s	270362×	0	valid
22.9s	8195×	3	valid
18.1s	19320×	2	valid
14.9s	49623×	0	unsamplable
7.4s	1371×	4	valid
3.3s	11263×	1	invalid
3.3s	18712×	0	invalid
1.5s	1725×	2	invalid
101.0ms	925×	0	precondition
47.0ms	64×	1	unsamplable
12.0ms	20×	3	invalid
4.0ms	2×	5	valid

Precisions

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

ival-pow: 1.9min (42.6% of total)

ival-mult: 26.1s (9.7% of total)

ival-sin: 21.8s (8.1% of total)

ival-cos: 21.6s (8% of total)

ival-div: 17.4s (6.5% of total)

backward-pass: 16.9s (6.3% of total)

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

ival-sub: 8.7s (3.2% of total)

ival-log: 6.2s (2.3% of total)

ival-exp: 6.2s (2.3% of total)

ival-sqrt: 4.8s (1.8% of total)

ival-neg: 3.9s (1.4% of total)

ival-<: 2.6s (1% of total)

...c/correct-round.rkt:121:19: 2.6s (1% of total)

const: 1.0s (0.4% of total)

ival-atan2: 975.0ms (0.4% of total)

ival-acos: 709.0ms (0.3% of total)

ival-pi: 659.0ms (0.2% of total)

ival-tan: 633.0ms (0.2% of total)

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

ival-atan: 441.0ms (0.2% of total)

ival-<=: 301.0ms (0.1% of total)

ival-cbrt: 291.0ms (0.1% of total)

ival-asin: 232.0ms (0.1% of total)

ival-fabs: 179.0ms (0.1% of total)

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

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

Bogosity

simplify2.7min (15.6%)

Algorithm

447×	egg-herbie

Rules

184460×	`fma-define`
119337×	`fma-neg`
103408×	`distribute-lft-in`
90298×	`*-commutative`
90032×	`distribute-rgt-in`

Stop Event

125×	saturated
321×	node limit
1×	unsound

Counts

146079 → 119931

soundness1.9min (11%)

Rules

90542×	`fma-define`
64640×	`log1p-expm1-u`
52061×	`*-commutative`
52027×	`distribute-lft-in`
50978×	`fma-neg`

Stop Event

15×	saturated
44×	fuel
256×	node limit
3×	unsound
8×	done

Compiler

Compiled 66302 to 19539 computations (70.5% saved)

localize1.5min (8.7%)

Results

23.0s	13033×	1	valid
18.4s	1875×	5	exit
12.8s	27557×	0	valid
8.1s	2766×	2	valid
3.9s	4595×	0	invalid
3.1s	507×	3	valid
1.5s	300×	1	invalid
457.0ms	47×	4	valid
5.0ms	8×	0	unsamplable

Compiler

Compiled 91642 to 7558 computations (91.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.1s

ival-mult: 8.0s (16.5% of total)

ival-pow: 7.4s (15.3% of total)

ival-sin: 7.4s (15.3% of total)

ival-cos: 6.7s (13.9% of total)

backward-pass: 4.5s (9.3% of total)

ival-div: 3.7s (7.8% of total)

ival-add: 1.6s (3.4% of total)

...c/correct-round.rkt:121:19: 1.2s (2.5% of total)

ival-sub: 1.1s (2.3% of total)

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

ival-sqrt: 987.0ms (2.1% of total)

ival-fma: 744.0ms (1.5% of total)

ival-exp: 572.0ms (1.2% of total)

ival-neg: 521.0ms (1.1% of total)

ival-hypot: 471.0ms (1% of total)

ival-log1p: 402.0ms (0.8% of total)

ival-atan2: 389.0ms (0.8% of total)

ival-cbrt: 369.0ms (0.8% of total)

const: 227.0ms (0.5% of total)

ival-atan: 187.0ms (0.4% of total)

ival-acos: 149.0ms (0.3% of total)

ival-tan: 145.0ms (0.3% of total)

ival-expm1: 130.0ms (0.3% of total)

ival-fabs: 94.0ms (0.2% of total)

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

ival-asin: 42.0ms (0.1% of total)

regimes59.8s (5.7%)

Counts

25426 → 923

Calls

155 calls:

3.8s	phi2
3.5s	phi1
3.4s	lambda2
3.2s	lambda1
3.1s	(-.f64 lambda1 lambda2)

Compiler

Compiled 13933 to 8964 computations (35.7% saved)

rewrite53.5s (5.1%)

Algorithm

197×	batch-egg-rewrite

Rules

127268×	`log1p-expm1-u`
92081×	`expm1-log1p-u`
52059×	`pow1`
47892×	`add-exp-log`
45702×	`add-log-exp`

Stop Event

193×	node limit
4×	unsound

Counts

2994 → 77916

prune52.3s (5%)

Counts: 189937 → 8439
Compiler: Compiled 588311 to 286067 computations (51.4% saved)

eval42.7s (4.1%)

Compiler: Compiled 8679022 to 838926 computations (90.3% saved)

series38.9s (3.7%)

Counts

2994 → 68163

Calls

17781 calls:

Time	Variable		Point	Expression
881.0ms	b	@	inf	(log (+ 1 (* 180 (/ (atan (/ (- (* (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)))))))) (* 2 (/ (* (cos (* angle (* (PI) 1/180))) (* (sin (* angle (* (PI) 1/180))) (- (pow b 2) (pow a 2)))) (* y-scale x-scale))))) (PI)))))
421.0ms	angle	@	0	(/ (- (- (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale) (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale)) (sqrt (+ (pow (- (/ (/ (+ (pow (* a (sin (* (/ angle 180) (PI)))) 2) (pow (* b (cos (* (/ angle 180) (PI)))) 2)) x-scale) x-scale) (/ (/ (+ (pow (* a (cos (* (/ angle 180) (PI)))) 2) (pow (* b (sin (* (/ angle 180) (PI)))) 2)) y-scale) y-scale)) 2) (pow (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale) 2)))) (/ (/ (* (* (* 2 (- (pow b 2) (pow a 2))) (sin (* (/ angle 180) (PI)))) (cos (* (/ angle 180) (PI)))) x-scale) y-scale))
412.0ms	x-scale	@	-inf	(/ (* x-scale (* y-scale (+ (* 2 (/ (* (pow a 2) (pow (sin (* 1/180 (* angle (PI)))) 2)) (pow x-scale 2))) (* 2 (/ (* (pow b 2) (pow (cos (* 1/180 (* angle (PI)))) 2)) (pow x-scale 2)))))) (* (cos (* 1/180 (* angle (PI)))) (* (sin (* 1/180 (* angle (PI)))) (- (pow b 2) (pow a 2)))))
377.0ms	angle	@	0	(/ (sqrt (* (* b (* (pow a 2) (neg b))) (* (* 8 (* b (/ (* (pow a 2) (neg b)) (pow (* x-scale y-scale) 2)))) (+ (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (- (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2)) (sqrt (+ (* (- (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2))) (- (/ (+ (pow (* a (sin (* angle (/ (PI) 180)))) 2) (pow (* b (cos (* angle (/ (PI) 180)))) 2)) (pow x-scale 2)) (/ (+ (pow (* a (cos (* angle (/ (PI) 180)))) 2) (pow (* b (sin (* angle (/ (PI) 180)))) 2)) (pow y-scale 2)))) (* (* (* 2 (- (pow b 2) (pow a 2))) (/ (* (sin (* angle (/ (PI) 180))) (cos (* angle (/ (PI) 180)))) (* x-scale y-scale))) (* (* 2 (- (pow b 2) (pow a 2))) (/ (* (sin (* angle (/ (PI) 180))) (cos (* angle (/ (PI) 180)))) (* x-scale y-scale))))))))))) (* b (/ (* (pow a 2) (neg b)) (pow (* x-scale y-scale) 2))))
362.0ms	x-scale	@	0	(sqrt (* (* 1/4 (* x-scale (sqrt 8))) (* (sqrt 2) (sqrt (+ (* (* a (cos (* 1/180 (* angle (PI))))) (* a (cos (* 1/180 (* angle (PI)))))) (* (* b (sin (* 1/180 (* angle (PI))))) (* b (sin (* 1/180 (* angle (PI)))))))))))

explain25.9s (2.5%)

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`#f`	sensitivity	1839	2
`+.f64`	`#f`	cancellation	1737	32
`sin.f64`	`#f`	sensitivity	1600	0
`sqrt.f64`	`#f`	oflow-rescue	1364	0
`-.f64`	`#f`	cancellation	922	13
`-.f64`	`#f`	nan-rescue	652	0
`log.f64`	`#f`	sensitivity	588	1
`/.f64`	`#f`	o/n	502	0
`/.f64`	`#f`	o/o	362	0
`/.f64`	`#f`	u/u	311	0
`*.f64`	`#f`	*no**	210	0
`/.f64`	`#f`	u/n	208	0
`exp.f64`	`#f`	sensitivity	157	25
`sqrt.f64`	`#f`	uflow-rescue	154	0
`*.f64`	`#f`	*nu**	121	0
`/.f64`	`#f`	n/o	97	0
`cbrt.f64`	`#f`	oflow-rescue	87	0
`cbrt.f64`	`#f`	uflow-rescue	39	0
`/.f64`	`#f`	n/u	38	0
`*.f64`	`#f`	*ou**	27	0
`*.f64`	`#f`	*uo**	25	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	16	2
`pow.f64`	`#f`	uflow-rescue	11	0
`pow.f64`	`#f`	sensitivity	9	2
`log.f64`	`#f`	oflow-rescue	6	0
`log.f64`	`(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))`	uflow-rescue	1	0
↳	`(+.f64 (exp.f64 a) (exp.f64 b))`	underflow	1
↳	`(exp.f64 a)`	underflow	130
↳	`(exp.f64 b)`	underflow	1
`sin.f64`	`(sin.f64 (/.f64 (-.f64 lambda1 lambda2) #s(literal 2 binary64)))`	cancellation	1	0

Confusion

	Predicted +	Predicted -
+	5751	74
-	1307	6180

Precision

0.8148200623406064

Recall

0.9872961373390557

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5751	39	35
-	1307	31	6149

Precision?

0.8122895622895623

Recall?

0.9939914163090129

Freqs

test

number	freq
0	6254
1	4664
2	1585
3	340
4	237
5	146
6	61
7	16
8	7
9	2

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	42	0	1
-	2	0	7

Precision?

0.9545454545454546

Recall?

0.9767441860465116

Results

5.1s	8320×	1	valid
3.1s	15710×	0	valid
2.7s	1930×	2	valid
1.7s	582×	3	valid
799.0ms	82×	4	valid

Compiler

Compiled 21932 to 3232 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0s

ival-sin: 1.8s (19.9% of total)

ival-mult: 1.3s (14.1% of total)

ival-cos: 1.2s (13.7% of total)

ival-div: 1.0s (11.5% of total)

ival-pow: 961.0ms (10.6% of total)

backward-pass: 773.0ms (8.5% of total)

ival-add: 443.0ms (4.9% of total)

ival-sub: 411.0ms (4.5% of total)

ival-log: 287.0ms (3.2% of total)

ival-sqrt: 201.0ms (2.2% of total)

ival-exp: 190.0ms (2.1% of total)

ival-neg: 102.0ms (1.1% of total)

ival-atan2: 72.0ms (0.8% of total)

const: 59.0ms (0.7% of total)

ival-tan: 48.0ms (0.5% of total)

ival-pi: 42.0ms (0.5% of total)

ival-atan: 34.0ms (0.4% of total)

ival-cbrt: 27.0ms (0.3% of total)

ival-acos: 21.0ms (0.2% of total)

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

ival-asin: 8.0ms (0.1% of total)

bsearch24.6s (2.3%)

Algorithm

338×	binary-search
67×	left-value

Stop Event

2×	predicate-same
336×	narrow-enough

Results

10.1s	10924×	1	valid
6.0s	28506×	0	valid
2.1s	1136×	3	valid
1.4s	1258×	2	valid
610.0ms	48×	4	valid
230.0ms	1921×	0	invalid

Compiler

Compiled 113169 to 76738 computations (32.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.9s

ival-cos: 3.5s (20.6% of total)

ival-sin: 3.3s (19.7% of total)

ival-mult: 3.0s (17.9% of total)

ival-pow: 1.7s (10.3% of total)

ival-div: 1.5s (9.1% of total)

ival-sub: 959.0ms (5.7% of total)

backward-pass: 741.0ms (4.4% of total)

ival-sqrt: 518.0ms (3.1% of total)

ival-add: 463.0ms (2.7% of total)

ival-atan2: 346.0ms (2% of total)

ival-exp: 129.0ms (0.8% of total)

ival-acos: 125.0ms (0.7% of total)

ival-neg: 109.0ms (0.6% of total)

ival-atan: 105.0ms (0.6% of total)

ival-tan: 96.0ms (0.6% of total)

const: 81.0ms (0.5% of total)

ival-pi: 51.0ms (0.3% of total)

ival-log: 40.0ms (0.2% of total)

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

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

analyze23.9s (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: 15.3s

ival-mult: 4.9s (32% of total)

ival-pow: 2.3s (15.1% of total)

ival-cos: 1.6s (10.2% of total)

ival-sin: 1.4s (8.9% of total)

ival-div: 1.1s (7% of total)

ival-add: 853.0ms (5.6% of total)

ival-sub: 852.0ms (5.6% of total)

ival-sqrt: 476.0ms (3.1% of total)

ival-neg: 361.0ms (2.4% of total)

ival-<: 321.0ms (2.1% of total)

...c/correct-round.rkt:121:19: 287.0ms (1.9% of total)

ival-atan2: 180.0ms (1.2% of total)

ival-asin: 99.0ms (0.6% of total)

ival-atan: 98.0ms (0.6% of total)

const: 94.0ms (0.6% of total)

ival-tan: 90.0ms (0.6% of total)

ival-pi: 78.0ms (0.5% of total)

ival-exp: 77.0ms (0.5% of total)

ival-and: 55.0ms (0.4% of total)

ival-log: 52.0ms (0.3% of total)

ival-acos: 38.0ms (0.2% of total)

ival-fabs: 32.0ms (0.2% of total)

backward-pass: 24.0ms (0.2% of total)

ival-cbrt: 17.0ms (0.1% of total)

ival-<=: 5.0ms (0% of total)

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

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

preprocess16.3s (1.5%)

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 56360 to 20620 computations (63.4% saved)

Herbie run

sample5.7min (32.5%)

simplify2.7min (15.6%)

soundness1.9min (11%)

localize1.5min (8.7%)

regimes59.8s (5.7%)

rewrite53.5s (5.1%)

prune52.3s (5%)

eval42.7s (4.1%)

series38.9s (3.7%)

explain25.9s (2.5%)

bsearch24.6s (2.3%)

analyze23.9s (2.3%)

preprocess16.3s (1.5%)

end0.0ms (0%)

Profiling