Details

analyze1.8s

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.140381%

sample40.0ms

Algorithm

intervals

Results

15.0ms	58×	body	1280	valid
7.0ms	40×	body	640	valid
6.0ms	138×	body	80	valid
1.0ms	10×	body	320	valid
1.0ms	10×	body	160	valid

simplify365.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series83.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
25.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824

prune189.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`associate-r`
19×	`add-cube-cbrt` `times-frac`
13×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp` `difference-of-squares`
7×	`associate-l`
4×	`tan-quot` `flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out--`
3×	`frac-times` `swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `div-exp` `sum-log` `pow-sqr` `pow-prod-up` `flip--` `div-inv`

Counts

4 → 103

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
4.0ms	(+ (sqrt 1.0) (tan x))
15.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))

series63.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
7.0ms	(+ (sqrt 1.0) (tan x))
41.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
9.0ms	(* (tan x) (tan x))

simplify65.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	490	1089
1	2418	957
2	5001	945

prune195.0ms

Filtered

78 candidates to 115 candidates (-47.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 0.0b

Counts

128 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(log (pow (exp 1) (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
8×	`tan-quot` `add-cbrt-cube`
7×	`log-prod`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
3×	`unpow-prod-down` `rem-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `log-div` `flip3--` `diff-log` `div-sub` `pow-exp` `log-pow` `flip--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 88

Calls

4 calls:

3.0ms	(- 1.0 (* (tan x) (tan x)))
3.0ms	(log (pow (exp 1) (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series108.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (* (tan x) (tan x)))
82.0ms	(log (pow (exp 1) (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
8.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

simplify154.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	256	688
1	905	592
2	4469	578
3	5001	560

prune146.0ms

Filtered

60 candidates to 100 candidates (-66.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	100	11	111

Merged error: 0.0b

Counts

111 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.3b	(* (tan x) (tan x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt`
6×	`tan-quot` `associate-r` `associate-l` `add-log-exp`
3×	`times-frac` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `diff-log` `associate-r/` `clear-num` `pow-sqr` `pow-prod-up` `flip--` `div-inv` `associate-/l/` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

4.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(/ (* (tan x) (sin x)) (cos x))
4.0ms	(* (tan x) (sin x))
5.0ms	(* (tan x) (tan x))

series49.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
12.0ms	(* (tan x) (sin x))
8.0ms	(* (tan x) (tan x))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	291	567
1	1265	503
2	5001	495

prune82.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	96	10	106

Merged error: 0.0b

Counts

106 → 10

regimes231.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

end0.0ms

analyze1.5s

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.140381%

sample1.0s

Algorithm

intervals

Results

397.0ms	1557×	body	1280	valid
223.0ms	1315×	body	640	valid
172.0ms	4240×	body	80	valid
70.0ms	578×	body	320	valid
26.0ms	310×	body	160	valid

Details

analyze1.8s

sample40.0ms

simplify365.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series83.0ms

simplify42.0ms

prune189.0ms

localize10.0ms

rewrite33.0ms

series63.0ms

simplify65.0ms

prune195.0ms

localize16.0ms

rewrite17.0ms

series108.0ms

simplify154.0ms

prune146.0ms

localize13.0ms

rewrite21.0ms

series49.0ms

simplify43.0ms

prune82.0ms

regimes231.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze1.5s

sample1.0s

Profiling