Details

sample148.0ms

Algorithm

intervals

Results

62.0ms	87×	body	1280	valid
37.0ms	22×	body	2560	valid
23.0ms	57×	body	640	valid
10.0ms	30×	body	320	valid
4.0ms	48×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.5b

localize8.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `tan-sum` `frac-sub` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

9.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series145.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(tan (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	192	420
1	538	319
2	2593	310
3	5001	255

prune117.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(* (tan x) (tan eps))
2.9b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3-+` `frac-add` `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` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

4.0ms	(+ (tan x) (tan eps))
12.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
5.0ms	(* (tan x) (tan eps))
54.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series740.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (tan x) (tan eps))
208.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
89.0ms	(* (tan x) (tan eps))
351.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify78.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	559	2915
1	2054	2366
2	5001	2345

prune415.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.1b	(* (tan x) (tan eps))
2.9b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`add-cube-cbrt`
10×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
6×	`tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `flip3--` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

5.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
4.0ms	(+ (tan x) (tan eps))
6.0ms	(* (tan x) (tan eps))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1 (- 1 (* (tan x) (tan eps))))
93.0ms	(+ (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
290.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	367	754
1	1426	679
2	5001	679

prune299.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (tan x) (tan eps)))
0.1b	(* (tan x) (tan eps))
2.3b	(log (exp (* (tan x) (tan eps))))
2.9b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
4×	`tan-quot` `expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`exp-prod` `exp-to-pow`
1×	`frac-times` `associate-r/` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

5.0ms	(exp (* (tan x) (tan eps)))
6.0ms	(* (tan x) (tan eps))
1.0ms	(log (exp (* (tan x) (tan eps))))
0.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(exp (* (tan x) (tan eps)))
92.0ms	(* (tan x) (tan eps))
92.0ms	(log (exp (* (tan x) (tan eps))))
290.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (log (exp (* (tan x) (tan eps)))))) (- (tan x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	228	561
1	667	496
2	2497	494
3	5001	490

prune238.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 13.5b

regimes186.0ms

Accuracy

82% (1.3b remaining)

Error of 15.8b against oracle of 14.5b and baseline of 21.8b

bsearch191.0ms

Steps

Iters	Range		Point
9	3.629416761052502e-123	1.276114475802425e-115	2.1114736186435238e-119
9	-3.988411557623274e-08	-4.1946683250978935e-14	-4.2497976182633953e-14

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	35
1	39	35

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.4s	3343×	body	1280	valid
1.1s	650×	body	2560	valid
708.0ms	1733×	body	640	valid
210.0ms	795×	body	320	valid
95.0ms	1127×	body	80	valid
66.0ms	352×	body	160	valid