Details

sample434.0ms

Algorithm

intervals

Results

83.0ms	41×	body	2560	valid
63.0ms	99×	body	1280	valid
17.0ms	52×	body	640	valid
7.0ms	30×	body	320	valid
3.0ms	17×	body	160	valid
1.0ms	17×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

22.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify55.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune254.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
2.2b	(- x (sin x))
26.9b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-prod` `fma-neg` `associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `pow1/3` `diff-log` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
7.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
4.0ms	(- x (sin x))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt x)
501.0ms	(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
33.0ms	(- x (sin x))
325.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	342	1106
1	1187	942
2	5001	897

prune274.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
64×	`add-cube-cbrt`
62×	`unpow-prod-down` `cube-prod`
42×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `fma-neg` `flip--`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 220

Calls

4 calls:

13.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
11.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
4.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series265.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
100.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
49.0ms	(- x (tan x))
35.0ms	(- x (sin x))

simplify101.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	853	2551
1	3624	2259
2	5001	2239

prune373.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
2.2b	(- x (tan x))
2.2b	(- x (sin x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 156

Calls

4 calls:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
4.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
49.0ms	(- x (tan x))
35.0ms	(- x (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	541	1431
1	1836	1207
2	5001	1207

prune383.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch69.0ms

Steps

Iters	Range		Point
10	9.558161037350472e-13	0.8818080259852756	0.027208711435501284
5	-0.041603525395973645	-0.015510049556855336	-0.026896790136361697

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.5s	1588×	body	2560	valid
1.9s	2762×	body	1280	valid
611.0ms	1826×	body	640	valid
210.0ms	945×	body	320	valid
77.0ms	509×	body	160	valid
40.0ms	370×	body	80	valid