Details

sample358.0ms

Algorithm

intervals

Results

16.0ms	422×	body	80	nan
12.0ms	240×	body	80	valid
9.0ms	253×	body	80	overflowed
2.0ms	18×	body	160	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 3.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.0b	(- (exp x) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series203.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify125.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune292.0ms

Filtered

135 candidates to 92 candidates (68.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
0.0b	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/l/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/r*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

19.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
19.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)))
176.0ms	(/ (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp (* 2.0 x))) (sqrt 1.0))) (- (exp x) 1.0))
47.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
14.0ms	(- (exp x) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	481	1464
1	2401	1163
2	5003	1124

prune277.0ms

Filtered

117 candidates to 82 candidates (70.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Merged error: 0b

Counts

121 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (exp x) 1.0) 3))
0.1b	(pow (- (exp x) 1.0) 3)
4.0b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
9×	`difference-of-squares`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`sqrt-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cube-div` `flip3--` `flip--`
3×	`pow-unpow`
2×	`cube-mult` `sub-neg` `cbrt-div` `diff-log` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 88

Calls

4 calls:

5.0ms	(cbrt (pow (- (exp x) 1.0) 3))
5.0ms	(pow (- (exp x) 1.0) 3)
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0ms	(- (exp x) 1.0)

series120.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (pow (- (exp x) 1.0) 3))
43.0ms	(pow (- (exp x) 1.0) 3)
46.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
17.0ms	(- (exp x) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	296	560
1	1075	533
2	5001	524

prune226.0ms

Filtered

100 candidates to 55 candidates (55.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	100	5	105

Merged error: 0b

Counts

105 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
14×	`sqrt-prod`
11×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
9×	`flip3--` `associate-r` `flip--`
8×	`frac-times` `add-cube-cbrt` `associate-/r/` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow1` `flip3-+` `flip-+`
5×	`times-frac` `associate-l` `associate-/l*`
4×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `diff-log` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out`
1×	`frac-2neg` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

16.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
18.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
7.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series425.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
264.0ms	(/ (- (exp (* 2.0 x)) 1.0) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
28.0ms	(- (exp (* 2.0 x)) 1.0)
36.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	537	1453
1	2767	1141
2	5001	1116

prune277.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	118	5	123

Merged error: 0b

Counts

123 → 5

regimes35.0ms

Accuracy

75.6% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.3b

bsearch33.0ms

Steps

Iters	Range		Point
6	-4.251583862655251e-05	-3.1026666635640823e-06	-1.7209794962066614e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	33	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

490.0ms	12670×	body	80	nan
314.0ms	7407×	body	80	valid
259.0ms	6836×	body	80	overflowed
70.0ms	697×	body	160	valid

Details

sample358.0ms

simplify95.0ms

prune4.0ms

localize14.0ms

rewrite34.0ms

series203.0ms

simplify125.0ms

prune292.0ms

localize14.0ms

rewrite51.0ms

series354.0ms

simplify66.0ms

prune277.0ms

localize16.0ms

rewrite24.0ms

series120.0ms

simplify40.0ms

prune226.0ms

localize13.0ms

rewrite51.0ms

series425.0ms

simplify66.0ms

prune277.0ms

regimes35.0ms

bsearch33.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling