Metrics for Herbie run

Date:	Sunday, June 2nd, 2024
Commit:	61eacaee on platforms
Hostname:	nightly with Racket 8.11.1
Seed:	2024154
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

soundness4.8min (26.4%)

Rules

787288×	`-lowering-.f32`
787288×	`-lowering-.f64`
460502×	`+-lowering-+.f32`
460502×	`+-lowering-+.f64`
333440×	`/-lowering-/.f32`

Stop Event

19×	saturated
245×	iter limit
38×	fuel
217×	node limit
16×	done

Compiler

Compiled 38778 to 20126 computations (48.1% saved)

sample4.4min (24%)

Results

1.5min	7822×	5	exit
1.4min	434310×	0	valid
11.4s	29190×	1	valid
2.8s	6739×	2	valid
1.2s	5758×	0	unsamplable
225.0ms	419×	3	valid
53.0ms	482×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.6min

ival-sin: 1.2min (46.9% of total)

ival-mult: 32.1s (20.6% of total)

ival-add: 19.5s (12.5% of total)

...c/correct-round.rkt:119:19: 6.0s (3.8% of total)

ival-div: 4.6s (3% of total)

backward-pass: 3.2s (2% of total)

ival-exp: 2.6s (1.7% of total)

ival-log: 2.4s (1.6% of total)

ival-sub: 2.4s (1.5% of total)

ival-sqrt: 1.9s (1.2% of total)

ival-cos: 1.2s (0.8% of total)

ival-asin: 1.1s (0.7% of total)

ival-pow: 1.0s (0.6% of total)

ival-atan2: 991.0ms (0.6% of total)

const: 788.0ms (0.5% of total)

ival-pi: 597.0ms (0.4% of total)

ival->: 516.0ms (0.3% of total)

ival-neg: 325.0ms (0.2% of total)

ival-<=: 323.0ms (0.2% of total)

ival-acosh: 283.0ms (0.2% of total)

ival-asinh: 244.0ms (0.2% of total)

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

ival-atanh: 195.0ms (0.1% of total)

ival->=: 143.0ms (0.1% of total)

ival-and: 86.0ms (0.1% of total)

Bogosity

simplify3.6min (19.5%)

Algorithm

453×	egg-herbie

Rules

1071954×	`-lowering-.f32`
1071954×	`-lowering-.f64`
643718×	`+-lowering-+.f32`
643718×	`+-lowering-+.f64`
370096×	`fma-lowering-fma.f64`

Stop Event

398×	iter limit
153×	saturated
300×	node limit

Counts

53736 → 53736

regimes1.5min (8%)

Counts

12654 → 958

Calls

128 calls:

36.8s	x
14.1s	(*.f64 #s(literal 2 binary64) (asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))))
12.9s	(sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
10.5s	(asin.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
1.9s	im

Compiler

Compiled 5903 to 3864 computations (34.5% saved)

rewrite1.3min (7.1%)

Algorithm

199×	batch-egg-rewrite

Rules

630150×	`-lowering-.f32`
630150×	`-lowering-.f64`
458986×	`/-lowering-/.f32`
458986×	`/-lowering-/.f64`
276642×	`+-lowering-+.f32`

Stop Event

6×	saturated
214×	iter limit
193×	node limit

Counts

2871 → 106640

localize46.6s (4.3%)

Results

14.2s	40472×	0	valid
13.0s	2317×	5	exit
2.3s	4333×	0	invalid
2.2s	2693×	1	valid
2.0s	823×	2	valid
154.0ms	268×	0	unsamplable
28.0ms	24×	3	valid
14.0ms	10×	4	valid
10.0ms	4×	1	unsamplable

Compiler

Compiled 59461 to 5479 computations (90.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.9s

ival-mult: 5.0s (23% of total)

ival-div: 2.8s (12.8% of total)

ival-pow: 2.2s (10.1% of total)

ival-add: 2.1s (9.5% of total)

backward-pass: 2.0s (9% of total)

...c/correct-round.rkt:119:19: 1.7s (7.7% of total)

ival-log: 1.5s (6.8% of total)

ival-sub: 881.0ms (4% of total)

ival-acos: 690.0ms (3.2% of total)

compiled-spec: 649.0ms (3% of total)

ival-atan2: 367.0ms (1.7% of total)

ival-sin: 354.0ms (1.6% of total)

ival-sqrt: 353.0ms (1.6% of total)

ival-cos: 313.0ms (1.4% of total)

ival-asin: 301.0ms (1.4% of total)

ival-exp: 214.0ms (1% of total)

const: 151.0ms (0.7% of total)

ival-fabs: 114.0ms (0.5% of total)

ival-copysign: 92.0ms (0.4% of total)

ival-neg: 86.0ms (0.4% of total)

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

ival-cbrt: 21.0ms (0.1% of total)

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

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

eval44.2s (4%)

Compiler: Compiled 7442797 to 471681 computations (93.7% saved)

prune27.1s (2.5%)

Counts: 198507 → 3557
Compiler: Compiled 195033 to 83373 computations (57.3% saved)

preprocess12.4s (1.1%)

Algorithm

112×	egg-herbie

Rules

64076×	`fnmadd-define`
61750×	`fma-define`
59546×	`sum3-define`
55566×	`fmsub-define`
47460×	`-lowering-.f32`

Stop Event

66×	saturated
56×	iter limit
46×	node limit

Compiler

Compiled 36702 to 11600 computations (68.4% saved)

bsearch11.3s (1%)

Algorithm

447×	binary-search
25×	left-value

Stop Event

19×	predicate-same
428×	narrow-enough

Results

6.1s	46142×	0	valid
1.6s	3803×	1	valid
347.0ms	708×	2	valid
14.0ms	35×	3	valid

Compiler

Compiled 108165 to 69281 computations (35.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.8s

ival-mult: 2.1s (36.4% of total)

ival-add: 634.0ms (11% of total)

ival-exp: 534.0ms (9.2% of total)

ival-sin: 500.0ms (8.6% of total)

ival-cos: 363.0ms (6.3% of total)

ival-log: 304.0ms (5.3% of total)

ival-sqrt: 239.0ms (4.1% of total)

ival-sub: 232.0ms (4% of total)

...c/correct-round.rkt:119:19: 221.0ms (3.8% of total)

ival-div: 177.0ms (3.1% of total)

backward-pass: 156.0ms (2.7% of total)

ival-atan2: 134.0ms (2.3% of total)

const: 71.0ms (1.2% of total)

ival-neg: 68.0ms (1.2% of total)

ival-copysign: 25.0ms (0.4% of total)

ival-fabs: 21.0ms (0.4% of total)

series10.3s (0.9%)

Counts

2871 → 53736

Calls

10596 calls:

Time	Variable		Point	Expression
336.0ms	x	@	0	(/ (+ 1 (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ (+ 1061405429/1000000000 (* 1061405429/1000000000 (* (fabs x) -3275911/10000000))) (+ 1 (* (* x x) -10731592879921/100000000000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ (* (fabs x) -3275911/10000000) -1))) 3)) (+ 1 (* (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ (+ 1061405429/1000000000 (* 1061405429/1000000000 (* (fabs x) -3275911/10000000))) (+ 1 (* (* x x) -10731592879921/100000000000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ (* (fabs x) -3275911/10000000) -1))) (- (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ (+ 1061405429/1000000000 (* 1061405429/1000000000 (* (fabs x) -3275911/10000000))) (+ 1 (* (* x x) -10731592879921/100000000000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ (* (fabs x) -3275911/10000000) -1))) 1))))
288.0ms	x	@	-inf	(log (/ (log x) x))
109.0ms	base	@	0	(* (log (log base)) 1)
95.0ms	x	@	0	(/ (- (/ (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (* (/ 1061405429/1000000000 (- 1 (pow (* (fabs x) -3275911/10000000) 2))) (+ 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ -1 (* (fabs x) -3275911/10000000)))) 4) (+ 1 (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ -1 (* (fabs x) -3275911/10000000)))) 2))) (/ 1 (+ 1 (pow (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (- 1 (* (fabs x) -3275911/10000000)))) (* (exp (* x x)) (+ -1 (* (fabs x) -3275911/10000000)))) 2)))) (- (/ (+ 31853699/125000000 (/ (+ -8890523/31250000 (/ (+ 1421413741/1000000000 (/ (+ -1453152027/1000000000 (/ 1061405429/1000000000 (+ 1 (* 3275911/10000000 (fabs x))))) (+ 1 (* 3275911/10000000 (fabs x))))) (+ 1 (* 3275911/10000000 (fabs x))))) (+ 1 (* 3275911/10000000 (fabs x))))) (* (exp (* x x)) (+ -1 (* (fabs x) -3275911/10000000)))) 1))
95.0ms	y.re	@	0	(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)

explain8.8s (0.8%)

Results

3.4s	24676×	0	valid
1.5s	3192×	1	valid
376.0ms	640×	2	valid
54.0ms	126×	5	exit
20.0ms	38×	3	valid

Compiler

Compiled 11865 to 1987 computations (83.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.2s

ival-mult: 981.0ms (30.4% of total)

ival-log: 403.0ms (12.5% of total)

ival-add: 302.0ms (9.4% of total)

ival-div: 271.0ms (8.4% of total)

backward-pass: 161.0ms (5% of total)

ival-sub: 157.0ms (4.9% of total)

...c/correct-round.rkt:119:19: 142.0ms (4.4% of total)

ival-sqrt: 132.0ms (4.1% of total)

ival-exp: 124.0ms (3.8% of total)

ival-asin: 97.0ms (3% of total)

compiled-spec: 89.0ms (2.8% of total)

ival-sin: 88.0ms (2.7% of total)

ival-cos: 81.0ms (2.5% of total)

const: 58.0ms (1.8% of total)

ival-atan2: 51.0ms (1.6% of total)

ival-fabs: 30.0ms (0.9% of total)

ival-pi: 17.0ms (0.5% of total)

ival-copysign: 16.0ms (0.5% of total)

ival-pow: 13.0ms (0.4% of total)

ival-neg: 10.0ms (0.3% of total)

analyze3.1s (0.3%)

Algorithm

58×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	86.3%	13.7%	0%	0%	0%	0
53.4%	46.1%	40.2%	13.7%	0%	0%	0%	1
62.8%	53.1%	31.4%	13.7%	0%	1.7%	0%	2
71.2%	58.4%	23.6%	13.7%	0%	4.3%	0%	3
77.4%	62%	18.1%	13.7%	0%	6.2%	0%	4
83.5%	66.8%	13.2%	13.7%	0%	6.3%	0%	5
85.8%	68.3%	11.3%	13.7%	0%	6.6%	0%	6
88.3%	70.3%	9.4%	13.7%	0%	6.6%	0%	7
89.9%	71.5%	8%	13.7%	0%	6.8%	0%	8
91.1%	72.5%	7.1%	13.7%	0%	6.8%	0%	9
92.6%	73.6%	5.9%	13.7%	0%	6.8%	0%	10
94%	74.7%	4.8%	13.7%	0%	6.8%	0%	11
94.5%	75.1%	4.4%	13.7%	0%	6.9%	0%	12

Compiler

Compiled 1558 to 790 computations (49.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.9s

ival-mult: 565.0ms (30.4% of total)

ival-add: 279.0ms (15% of total)

...c/correct-round.rkt:119:19: 201.0ms (10.8% of total)

ival-log: 135.0ms (7.3% of total)

ival-div: 124.0ms (6.7% of total)

ival-sqrt: 122.0ms (6.6% of total)

ival-sub: 103.0ms (5.5% of total)

ival-pow: 80.0ms (4.3% of total)

ival-atan2: 71.0ms (3.8% of total)

ival-exp: 64.0ms (3.4% of total)

ival-sin: 23.0ms (1.2% of total)

const: 22.0ms (1.2% of total)

ival->: 16.0ms (0.9% of total)

ival-cos: 15.0ms (0.8% of total)

ival-<=: 12.0ms (0.6% of total)

ival-neg: 9.0ms (0.5% of total)

ival-pi: 8.0ms (0.4% of total)

backward-pass: 6.0ms (0.3% of total)

ival-and: 2.0ms (0.1% of total)

ival-asin: 1.0ms (0.1% of total)

ival-atanh: 1.0ms (0.1% of total)

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

ival->=: 0.0ms (0% of total)

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

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

Herbie run

soundness4.8min (26.4%)

sample4.4min (24%)

simplify3.6min (19.5%)

regimes1.5min (8%)

rewrite1.3min (7.1%)

localize46.6s (4.3%)

eval44.2s (4%)

prune27.1s (2.5%)

preprocess12.4s (1.1%)

bsearch11.3s (1%)

series10.3s (0.9%)

explain8.8s (0.8%)

analyze3.1s (0.3%)

end0.0ms (0%)

Profiling