Details

sample164.0ms

Algorithm

intervals

Results

88.0ms	106×	body	1280	valid
29.0ms	65×	body	640	valid
24.0ms	14×	body	2560	valid
6.0ms	21×	body	320	valid
4.0ms	40×	body	80	valid
3.0ms	10×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
3.1b	(tan (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (tan (+ x eps)) (tan x))
49.0ms	(tan (+ x eps))

simplify83.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199

prune90.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series923.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
92.0ms	(+ (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
528.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	397	1052
1	1432	1007
2	5001	996

prune279.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(exp (* (tan x) (tan eps)))
2.9b	(log (exp (* (tan x) (tan eps))))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`tan-quot`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`exp-prod` `exp-to-pow` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `times-frac` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
4.0ms	(exp (* (tan x) (tan eps)))
1.0ms	(log (exp (* (tan x) (tan eps))))
72.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

series650.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (tan x) (tan eps))
122.0ms	(exp (* (tan x) (tan eps)))
89.0ms	(log (exp (* (tan x) (tan eps))))
347.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (exp (* (tan x) (tan eps)))))) (tan x))

simplify75.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	271	685
1	811	627
2	2808	613
3	5001	613

prune244.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (tan x))
0.2b	(pow (exp (tan x)) (tan eps))
2.9b	(log (pow (exp (tan x)) (tan eps)))
3.3b	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
7×	`log-prod` `add-log-exp`
6×	`unpow-prod-down` `exp-prod`
5×	`pow1` `add-exp-log`
4×	`pow-pow` `add-cbrt-cube`
3×	`pow-unpow` `rem-log-exp`
2×	`pow-to-exp` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`tan-quot` `sub-neg` `flip3--` `times-frac` `diff-log` `log-pow` `frac-sub` `flip--` `rem-exp-log` `distribute-lft-out--`

Counts

4 → 65

Calls

4 calls:

1.0ms	(exp (tan x))
3.0ms	(pow (exp (tan x)) (tan eps))
2.0ms	(log (pow (exp (tan x)) (tan eps)))
57.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

series840.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(exp (tan x))
166.0ms	(pow (exp (tan x)) (tan eps))
177.0ms	(log (pow (exp (tan x)) (tan eps)))
467.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (log (pow (exp (tan x)) (tan eps))))) (tan x))

simplify94.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	303	735
1	903	675
2	3172	654
3	5001	650

prune224.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.7b

regimes165.0ms

Accuracy

87.8% (0.9b remaining)

Error of 15.3b against oracle of 14.4b and baseline of 21.7b

bsearch168.0ms

Steps

Iters	Range		Point
10	7.236268304871825e-61	4.1125112799483e-50	3.029775318592972e-50
6	-4.443298397159394e-57	-5.6940246774022445e-58	-1.524092928575051e-57

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	16
1	32	16

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.7s	3329×	body	1280	valid
1.1s	631×	body	2560	valid
882.0ms	1823×	body	640	valid
227.0ms	747×	body	320	valid
110.0ms	1095×	body	80	valid
77.0ms	375×	body	160	valid