Metrics for Herbie run

Date:	Friday, April 5th, 2024
Commit:	9a443234 on explanations-eval-top3
Hostname:	nightly with Racket 8.11.1
Seed:	2024096
Parameters:	256 points for 4 iterations
Flags:	`reduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionssetup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:numericsrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:proofs` default

localize2.3min (23.4%)

Compiler: Compiled 39225 to 20352 computations (48.1% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.7min
Operation ival-pow, time spent: 27.3s, 26.0% of total-time
Operation ival-mult, time spent: 17.7s, 17.0% of total-time
Operation composed, time spent: 10.7s, 10.0% of total-time
Operation ival-div, time spent: 9.9s, 9.0% of total-time
Operation ival-add, time spent: 6.1s, 6.0% of total-time
Operation ival-tan, time spent: 6.0s, 6.0% of total-time
Operation ival-cos, time spent: 4.8s, 5.0% of total-time
Operation ival-log, time spent: 3.8s, 4.0% of total-time
Operation ival-sqrt, time spent: 3.7s, 4.0% of total-time
Operation ival-sin, time spent: 3.4s, 3.0% of total-time
Operation ival-sub, time spent: 2.9s, 3.0% of total-time
Operation ival-asin, time spent: 2.3s, 2.0% of total-time
Operation ival-exp, time spent: 2.0s, 2.0% of total-time
Operation const, time spent: 1.9s, 2.0% of total-time
Operation ival-acos, time spent: 1.2s, 1.0% of total-time
Operation ival-cbrt, time spent: 559.0ms, 1.0% of total-time
Operation ival-neg, time spent: 479.0ms, 0.0% of total-time
Operation ival-pi, time spent: 189.0ms, 0.0% of total-time
Operation ival-fabs, time spent: 10.0ms, 0.0% of total-time
Operation ival-e, time spent: 3.0ms, 0.0% of total-time

sample1.9min (19.5%)

Results

46.1s	179509×	256	valid
14.4s	67709×	256	invalid
9.7s	42808×	256	infinite
7.7s	10831×	1024	valid
7.1s	9312×	2048	valid
3.6s	8459×	512	valid
5.3s	7447×	1024	invalid
1.9s	4094×	512	invalid
2.2s	1963×	4096	valid
1.0s	777×	8192	valid
2.9s	772×	4096	infinite
1.8s	706×	2048	infinite
311.0ms	420×	1024	infinite
157.0ms	379×	512	infinite
37.0ms	180×	256	unsamplable
73.0ms	108×	2048	invalid
6.0ms	7×	8192	exit

Precisions

Click to see histograms. Total time spent on operations: 1.1min

Operation ival-mult, time spent: 18.5s, 28.0% of total-time

Operation ival-div, time spent: 10.3s, 16.0% of total-time

Operation ival-pow, time spent: 6.7s, 10.0% of total-time

Operation ival-tan, time spent: 5.5s, 8.0% of total-time

Operation ival-sub, time spent: 4.1s, 6.0% of total-time

Operation ival-sin, time spent: 3.8s, 6.0% of total-time

Operation ival-add, time spent: 3.5s, 5.0% of total-time

Operation ival-sqrt, time spent: 3.0s, 5.0% of total-time

Operation ival-exp, time spent: 2.7s, 4.0% of total-time

Operation const, time spent: 1.4s, 2.0% of total-time

Operation ival-cos, time spent: 1.4s, 2.0% of total-time

Operation ival-neg, time spent: 1.2s, 2.0% of total-time

Operation composed, time spent: 957.0ms, 1.0% of total-time

Operation ival-acos, time spent: 890.0ms, 1.0% of total-time

Operation ival-pi, time spent: 545.0ms, 1.0% of total-time

Operation ival-log, time spent: 535.0ms, 1.0% of total-time

Operation ival-asin, time spent: 236.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 139.0ms, 0.0% of total-time

Operation ival-<, time spent: 112.0ms, 0.0% of total-time

Operation ival-and, time spent: 19.0ms, 0.0% of total-time

Bogosity

eval1.1min (11.2%)

Compiler: Compiled 2975628 to 1954463 computations (34.3% saved)

regimes55.7s (9.4%)

Counts

9606 → 701

Calls

152 calls:

5.1s	l
3.5s	t
2.9s	EAccept
2.3s	EDonor
2.1s	Ev

Compiler

Compiled 8042 to 6262 computations (22.1% saved)

simplify47.8s (8.1%)

Algorithm

149×	egg-herbie

Rules

101570×	`fma-define`
81254×	`associate-r`
80434×	`*-commutative`
75160×	`times-frac`
69626×	`distribute-lft-in`

Stop Event

31×	saturated
118×	node limit
29×	fuel
2×	done

Counts

68484 → 57607

Compiler

Compiled 11432 to 7644 computations (33.1% saved)

soundness46.6s (7.9%)

Rules

98152×	`fma-define`
77094×	`times-frac`
76944×	`associate-r`
63988×	`*-commutative`
54686×	`distribute-lft-in`

Stop Event

7×	saturated
163×	node limit
1×	unsound

Compiler

Compiled 29581 to 18254 computations (38.3% saved)

preprocess30.9s (5.2%)

Algorithm

31×	egg-herbie

Rules

39452×	`fma-define`
26360×	`fma-neg`
16974×	`times-frac`
15822×	`unsub-neg`
14432×	`distribute-lft-in`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`#f`	cancellation	523	0
`cos.f64`	`#f`	sensitivity	423	0
`sqrt.f64`	`#f`	oflow-rescue	372	0
`acos.f64`	`(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))`	sensitivity	254	1
`+.f64`	`#f`	nan-rescue	245	0
`pow.f64`	`#f`	oflow-rescue	131	0
`tan.f64`	`(tan.f64 (*.f64 (PI.f64) l))`	sensitivity	130	0
`asin.f64`	`(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))`	sensitivity	128	0
`-.f64`	`#f`	nan-rescue	128	0
`sqrt.f64`	`#f`	uflow-rescue	119	0
`*.f64`	`#f`	*no**	101	0
`*.f64`	`#f`	*uo**	91	0
`pow.f64`	`(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))`	sensitivity	84	31
`cos.f64`	`(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))`	oflow-rescue	46	0
↳	`(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)`	overflow	46
↳	`(/.f64 (*.f64 K (+.f64 m n)) 2)`	overflow	46
↳	`(*.f64 K (+.f64 m n))`	overflow	46
`+.f64`	`(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))`	cancellation	43	0
`/.f64`	`#f`	o/o	38	0
`*.f64`	`(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))`	*ou**	33	0
↳	`(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))`	overflow	72
↳	`(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))`	overflow	69
↳	`(pow.f64 t 3)`	overflow	82
↳	`(/.f64 (pow.f64 t 3) (*.f64 l l))`	overflow	83
↳	`(*.f64 l l)`	overflow	66
↳	`(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)`	underflow	65
↳	`(pow.f64 (/.f64 k t) 2)`	underflow	65
↳	`(/.f64 k t)`	underflow	24
`pow.f64`	`(pow.f64 (/.f64 d h) (/.f64 1 2))`	uflow-rescue	32	0
↳	`(/.f64 d h)`	underflow	32
`/.f64`	`#f`	n/o	22	0
`/.f64`	`(/.f64 (pow.f64 t 3) (*.f64 l l))`	u/u	19	0
↳	`(pow.f64 t 3)`	underflow	78
↳	`(*.f64 l l)`	underflow	51
`log.f64`	`(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f)))) (-.f64 (exp.f64 (.f64 (/.f64 (PI.f64) 4) f)) (exp.f64 (neg.f64 (.f64 (/.f64 (PI.f64) 4) f))))))`	sensitivity	7	0
`/.f64`	`(/.f64 (.f64 M D) (.f64 2 d))`	o/n	7	0
↳	`(*.f64 M D)`	overflow	23
`exp.f64`	`(exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT))`	sensitivity	2	1

Confusion

	Predicted +	Predicted -
+	1603	282
-	1123	4928

Precision

0.5880410858400587

Recall

0.8503978779840848

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1603	2	280
-	1123	33	4895

Precision?

0.5813111191597248

Recall?

0.8514588859416445

Stop Event

8×	saturated
23×	node limit

Compiler

Compiled 54718 to 33716 computations (38.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.5s

Operation ival-mult, time spent: 2.6s, 27.0% of total-time

Operation ival-div, time spent: 1.4s, 15.0% of total-time

Operation ival-pow, time spent: 1.3s, 14.0% of total-time

Operation ival-tan, time spent: 796.0ms, 8.0% of total-time

Operation ival-sqrt, time spent: 576.0ms, 6.0% of total-time

Operation ival-add, time spent: 516.0ms, 5.0% of total-time

Operation ival-sin, time spent: 442.0ms, 5.0% of total-time

Operation ival-sub, time spent: 434.0ms, 5.0% of total-time

Operation ival-exp, time spent: 390.0ms, 4.0% of total-time

Operation ival-cos, time spent: 387.0ms, 4.0% of total-time

Operation const, time spent: 236.0ms, 2.0% of total-time

Operation composed, time spent: 198.0ms, 2.0% of total-time

Operation ival-neg, time spent: 136.0ms, 1.0% of total-time

Operation ival-log, time spent: 72.0ms, 1.0% of total-time

Operation ival-acos, time spent: 49.0ms, 1.0% of total-time

Operation ival-pi, time spent: 32.0ms, 0.0% of total-time

Operation ival-asin, time spent: 8.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 5.0ms, 0.0% of total-time

prune26.4s (4.5%)

Counts: 87324 → 3172
Compiler: Compiled 154333 to 107691 computations (30.2% saved)

rewrite26.0s (4.4%)

Algorithm

118×	batch-egg-rewrite

Rules

68192×	`log1p-expm1-u`
49135×	`expm1-log1p-u`
30960×	`prod-diff`
29995×	`add-exp-log`
29886×	`add-log-exp`

Stop Event

117×	node limit
1×	unsound

Counts

1256 → 35416

bsearch13.4s (2.3%)

Algorithm

312×	binary-search
71×	left-value

Stop Event

9×	predicate-same
303×	narrow-enough

Results

7.4s	28985×	256	valid
2.1s	6087×	256	infinite
1.3s	5011×	256	invalid
328.0ms	384×	1024	valid
92.0ms	153×	2048	valid
60.0ms	153×	512	valid
199.0ms	68×	4096	valid
88.0ms	37×	8192	valid
15.0ms	36×	512	infinite
10.0ms	23×	1024	invalid
16.0ms	21×	1024	infinite
3.0ms	12×	512	invalid
10.0ms	12×	2048	infinite
1.0ms	1×	8192	exit

Compiler

Compiled 90503 to 68842 computations (23.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.1s

Operation ival-mult, time spent: 1.8s, 25.0% of total-time

Operation ival-div, time spent: 1.4s, 19.0% of total-time

Operation ival-pow, time spent: 1.1s, 15.0% of total-time

Operation ival-add, time spent: 615.0ms, 9.0% of total-time

Operation ival-sub, time spent: 454.0ms, 6.0% of total-time

Operation ival-sin, time spent: 452.0ms, 6.0% of total-time

Operation ival-tan, time spent: 368.0ms, 5.0% of total-time

Operation ival-sqrt, time spent: 284.0ms, 4.0% of total-time

Operation ival-exp, time spent: 226.0ms, 3.0% of total-time

Operation ival-neg, time spent: 162.0ms, 2.0% of total-time

Operation ival-cos, time spent: 160.0ms, 2.0% of total-time

Operation const, time spent: 139.0ms, 2.0% of total-time

Operation composed, time spent: 44.0ms, 1.0% of total-time

Operation ival-fabs, time spent: 6.0ms, 0.0% of total-time

Operation ival-pi, time spent: 4.0ms, 0.0% of total-time

series12.7s (2.1%)

Counts

1256 → 33068

Calls

8712 calls:

Time	Variable		Point	Expression
251.0ms	a	@	0	(/ a (+ 1 (* k (+ 10 k))))
231.0ms	f	@	0	(* (/ 1 (/ (PI) 4)) (- (log 2) (log (* f (* (PI) 1/2)))))
165.0ms	U*	@	inf	(sqrt (* 2 (* n (* U (+ (* n (* (pow (/ l Om) 2) (- U* U))) (+ (* (* l (/ l Om)) -2) t))))))
160.0ms	NdChar	@	0	(/ NdChar (+ 1 (pow (sqrt (E)) (* 2 (/ (+ (+ Vef (- mu Ec)) EDonor) KbT)))))
139.0ms	t	@	inf	(/ 1 (/ (sqrt (+ (* (* (sqrt (+ (* l l) (* (* t (sqrt 2)) (* t (sqrt 2))))) (sqrt (/ (+ x 1) (+ x -1)))) (* (sqrt (+ (* l l) (* (* t (sqrt 2)) (* t (sqrt 2))))) (sqrt (/ (+ x 1) (+ x -1))))) (* l l))) (* t (sqrt 2))))

analyze11.9s (2%)

Algorithm

31×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	98.2%	1.8%	0%	0%	0%	0
19.7%	19.3%	78.9%	1.8%	0%	0%	0%	1
24.2%	23.3%	73.2%	1.8%	0%	1.6%	0%	2
29.6%	27.4%	65.2%	1.8%	0%	5.6%	0%	3
33.6%	30.4%	60.2%	1.8%	0%	7.3%	0.4%	4
35.9%	32.4%	57.9%	1.8%	0%	7.3%	0.6%	5
40.2%	36.2%	53.9%	1.8%	0%	7.4%	0.7%	6
45%	40.3%	49.1%	1.8%	0%	8%	0.8%	7
47.4%	41.8%	46.4%	1.8%	0%	9.2%	0.9%	8
50.2%	44.1%	43.7%	1.8%	0%	9.5%	0.9%	9
51.3%	44.9%	42.6%	1.8%	0%	9.7%	1%	10
53%	46.1%	40.9%	1.8%	0%	10.2%	1%	11
54.7%	47.3%	39.1%	1.8%	0%	10.8%	1%	12

Compiler

Compiled 845 to 607 computations (28.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.5s

Operation ival-mult, time spent: 1.8s, 28.0% of total-time

Operation ival-pow, time spent: 1.2s, 18.0% of total-time

Operation ival-div, time spent: 920.0ms, 14.0% of total-time

Operation ival-sqrt, time spent: 542.0ms, 8.0% of total-time

Operation ival-sub, time spent: 468.0ms, 7.0% of total-time

Operation ival-add, time spent: 353.0ms, 5.0% of total-time

Operation ival-sin, time spent: 257.0ms, 4.0% of total-time

Operation ival-tan, time spent: 242.0ms, 4.0% of total-time

Operation const, time spent: 168.0ms, 3.0% of total-time

Operation ival-cos, time spent: 160.0ms, 2.0% of total-time

Operation ival-neg, time spent: 88.0ms, 1.0% of total-time

Operation ival-acos, time spent: 77.0ms, 1.0% of total-time

Operation ival-exp, time spent: 75.0ms, 1.0% of total-time

Operation ival-pi, time spent: 53.0ms, 1.0% of total-time

Operation ival-asin, time spent: 23.0ms, 0.0% of total-time

Operation ival-<, time spent: 19.0ms, 0.0% of total-time

Operation ival-fabs, time spent: 17.0ms, 0.0% of total-time

Operation ival-log, time spent: 11.0ms, 0.0% of total-time

Operation ival-and, time spent: 3.0ms, 0.0% of total-time

Operation composed, time spent: 0.0ms, 0.0% of total-time

Herbie run

localize2.3min (23.4%)

sample1.9min (19.5%)

eval1.1min (11.2%)

regimes55.7s (9.4%)

simplify47.8s (8.1%)

soundness46.6s (7.9%)

preprocess30.9s (5.2%)

prune26.4s (4.5%)

rewrite26.0s (4.4%)

bsearch13.4s (2.3%)

series12.7s (2.1%)

analyze11.9s (2%)

end21.0ms (0%)

Profiling