Details

sample147.0ms

Algorithm

intervals

Results

69.0ms	260×	body	10240	exit
34.0ms	94×	body	1280	valid
21.0ms	84×	body	640	valid
6.0ms	38×	body	320	valid
2.0ms	20×	body	160	valid
2.0ms	20×	body	80	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	59	9
5	174	9
6	1153	9
7	5001	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
2.2b	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
5.4b	(- (exp x) (exp (- x)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`times-frac`
14×	`add-cube-cbrt`
7×	`distribute-lft-out` `add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`associate-/r*`
3×	`pow1`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `tanh-undef` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 73

Calls

3 calls:

5.0ms	(+ (exp x) (exp (- x)))
23.0ms	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
6.0ms	(- (exp x) (exp (- x)))

series136.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (exp x) (exp (- x)))
73.0ms	(/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))
40.0ms	(- (exp x) (exp (- x)))

simplify237.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	281	936
1	947	870
2	4970	860
3	5003	860

prune162.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize2.0ms

Local error

Found 1 expressions with local error:

0.0b

(tanh x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `tanh-def` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(tanh x)

series71.0ms

Counts

1 → 3

Calls

1 calls:

71.0ms

(tanh x)

simplify74.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	48
1	195	45
2	599	45
3	2891	45
4	5002	45

prune30.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tanh x)) (cbrt (tanh x)))
0.6b	(cbrt (tanh x))
0.6b	(cbrt (tanh x))
0.6b	(cbrt (tanh x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `tanh-def`
9×	`frac-times` `pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

8.0ms	(* (cbrt (tanh x)) (cbrt (tanh x)))
1.0ms	(cbrt (tanh x))
1.0ms	(cbrt (tanh x))
1.0ms	(cbrt (tanh x))

series742.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* (cbrt (tanh x)) (cbrt (tanh x)))
183.0ms	(cbrt (tanh x))
178.0ms	(cbrt (tanh x))
179.0ms	(cbrt (tanh x))

simplify118.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	259	769
1	807	701
2	4106	670
3	5001	662

prune212.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* 2/15 (pow x 5)))
0.0b	(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
0.1b	(* 2/15 (pow x 5))
0.1b	(* 1/3 (pow x 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `sub-neg` `flip3--` `flip3-+` `unpow3` `associate--l+` `flip--` `flip-+`

Counts

4 → 81

Calls

4 calls:

2.0ms	(+ x (* 2/15 (pow x 5)))
12.0ms	(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
5.0ms	(* 2/15 (pow x 5))
6.0ms	(* 1/3 (pow x 3))

series256.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ x (* 2/15 (pow x 5)))
58.0ms	(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
51.0ms	(* 2/15 (pow x 5))
35.0ms	(* 1/3 (pow x 3))

simplify48.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	314	427
1	1376	401
2	5001	396

prune183.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes23.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.5b

bsearch56.0ms

Steps

Iters	Range		Point
7	0.0017067078276629334	0.029742437103729882	0.0017859743216340305
7	-0.04371045001551677	-0.0019174381104543623	-0.004526963234389435

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	7562×	body	10240	exit
1.2s	3242×	body	1280	valid
583.0ms	2402×	body	640	valid
210.0ms	1254×	body	320	valid
78.0ms	668×	body	160	valid
34.0ms	434×	body	80	valid